Non-Linear Optical Properties of Matter

In this chapter we give an introduction to the theory of linear and nonlinear optics. We show how the response of a molecule to an external oscillating electric field can be described in terms of intrinsic properties of the molecules, namely the (hyper)polarizabilities. We outline how these properties are described in the case of exact states by considering the time-development of the exact state in the presence of a time-dependent electric field. Approximations introduced in theoretical studies of nonlinear optical properties are introduced, in particular the separation of electronic and nuclear degrees of freedom which gives rise to the partitioning of the (hyper)polarizabilities into electronic and vibrational contributions. Different approaches for calculating (hyper)polarizabilities are discussed, with a special focus on the electronic contributions in most cases. We end with a brief discussion of the connection between the microscopic responses of an individual molecule to the experimentally observed responses from a molecular ensemble

A review of methods for calculating vibrational contributions to linear and nonlinear optical properties is presented. Our aim is to provide an overview of the various approaches that have been developed using illustrative equations supplemented with references to the detailed formulations. The treatment of electrical and mechanical anharmonicity is considered in some detail for resonant as well as non-resonant processes. Issues such as the choice of basis set, the treatment of electron correlation, and the convergence of perturbation expansions are examined. Although much of the presentation is general, there is a special emphasis on organic pi-conjugated systems

The sum-over-states technique which is extensively used in calculations of nonlinear optical properties, is presented and discussed. We focus on the electronic contributions to first- and second-order hyperpolarizability. The SOS approach to the calculation of the multiphoton absorption is also discussed. The various approximations to exact sum-over-states formulae are presented. In particular, we describe the so-called few-levels models, which are widely used in qualitative analysis of nonlinear electrical properties

We review Kohn–Sham density-functional theory for time-dependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and the Ehrenfest principle, alternatively the quasi-energy ansatz. While the theory retains the adiabatic approximation, implying that the time-dependency of the functional is obtained only implicitly—through the time-dependency of the density itself rather than through the form of the exchange-correlation functionals—our implementation generalizes previous time-dependent approaches in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). Thus, the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange–correlation at the generalized gradient-approximation level and fractional exact Hartree–Fock exchange. We also review some recent progress in time-dependent density functional theory for open-shell systems, in particular spin-restricted and spin restricted-unrestricted formalisms for property calculations. We highlight a sample of applications of the theory

It is an experimental fact that light propagation in a medium is sensitively dependent on the shape and intensity of the optical pulse as well as on the electronic and vibrational structure of the basic molecular units. We review in this paper results of systematic studies of this problem for isotropic media. Our theoretical approach is based on numerical solutions of the density matrix and Maxwell’s equations and a quantum mechanical account of the complexity of the many-level electron-nuclear medium. This allows to accommodate a variety of non-linear effects which accomplish the propagation of strong light pulses. Particular attention is paid to the understanding of the role of coherent and sequential excitations of electron-nuclear degrees of freedoms. We highlight the combination of quantum chemistry with classical pulse propagation which allows to estimate the optical transmission from cross sections of multi-photon absorption processes and from considerations of propagation effects, saturation and pulse effects. It is shown that in the non-linear regime it is often necessary to account simultaneously for coherent one-step and incoherent step-wise multi-photon absorption, as well as for off-resonant excitations even when resonance conditions prevail. The dynamic theory of non-linear propagation of a few interacting intense light pulses has been successfully applied to study, for example, frequency-upconversion cavity-less lasing in a chromophore solution, namely in an organic stilbenechromophore 4-[N-(2-hydroxyethyl)-N-(methyl)amino phenyl]-4′-(6-hydroxyhexyl sulphonyl) dissolved in dimethyl sulphoxide. Furthermore, the theory has been used to explain observed differences between spectral shapes of one- and two-photon absorption in the di-phenyl-amino-nitro-stilbene molecule. The present simulations evidence that the reason for this effect is the competition between two-step and coherent two-photon absorption processes

We discuss cooperative and collective behavior resulting from classical electrostatic intermolecular interactions in molecular materials with negligible intermolecular overlap. With reference to materials based on push-pull chromophores, we discuss the merits of several approximation schemes for the calculation of linear and non-linear optical susceptibilities. Collective and cooperative behavior is recognized in important deviations of the material properties from the oriented gas approximation scheme, and/or from the exciton model. Extreme collective and cooperative behavior in attractive clusters is discussed, where bistable behavior and the phenomenon of multielectron-transfer appear

The fundamental aspects of response theory for the multiconfigurational self-consistent field electronic structure method coupled to molecular mechanics force fields are outlined. An overwiew of the theoretical developments presented in the work by Poulsen et al. is given. Poulsen et al. have developed multiconfigurational self-consistent field molecular mechanics (MCSCF/MM) response methods to include third order molecular properties and these approaches are discussed

We review the theoretical approaches based on the perturbation theory, namely few-states approximations. These approaches are extensively used in the description of the solvent effects on nonlinear response of molecular systems. The connection between the nonlinear optical response and solvatochromic behavior of the donor-acceptor π-conjugated molecules is considered. The general relations between molecular (hyper)polarizabilities and two-photon absorption for the positively and negatively solvatochromic compounds are presented

This chapter presents a review of the direct implantation of symmetry into calculations of carbon nanotubes (CNTs) second order nonlinear optical properties (NLO). Emphasis is given to potentiality of the method to estimate quantitatively the magnitude of first hyperpolarizability for several CNTs topologies. The main advantage of performing calculations with symmetrized eigenfunctions, relies on the direct identification of the state-to-state transitions contributing to the hyperpolarizability. An estimated value of β ∼ 10^-30esu for the non-resonant hyperpolarizability of chiral CNTs is obtained

The orientation of the nonlinear optical chromophore in a guest-host polymer system under the application of an external electric field plays an important role in the electro-optic activity in the material. The process of electric field poling of nonlinear optical chromophores in polymer systems has been studied through both Monte Carlo simulations and atomistic molecular modeling simulations. We review the progress of simulations in this area as well as describe our efforts and progress in understanding the process of electric field poling at an atomistic level of theory

This chapter deals with recent and important developments in the field of the molecular design of ionic organic materials with and without metals for second-order nonlinear optics. The first section discusses 1) the origin of optical nonlinearity, 2) the relationship between microscopic and macroscopic polarizabilities and 3) the importance of ionic chromophores as second-order nonlinear optical (NLO) materials. The second section reviews 4) the current experimental and theoretical developments in the design of dipolar and octupolar ionic chromophores for second-order nonlinear optics and 5) the progress on zwitterionic second-order NLO materials. The third section presents 6) possible device applications based on ionic chromophores

Different techniques to characterize the strength of the second- and third-order nonlinear optical response are presented, with particular emphasis on the relationship between the macroscopic measurable quantities and the intrinsic molecular nonlinear properties

We present a review of the main results reported in the literature regarding the third-order nonlinear optical response of nanocomposite media consisting of noble metal nanoparticles surrounded by a dielectric host. This phenomenon, known as optical Kerr effect, can be characterized by the intensity-dependent complex optical index of the material or, equivalently, its complex third-order susceptibility. The theoretical basis of the linear and nonlinear optical properties of metal nanoparticles and nanocomposite media are described first. The different third-order optical phenomena which have been observed in such materials are then examined. The dependence of the nonlinear properties on morphological parameters – nature of the dielectric host, metal concentration, particle size and shape – as well as on laser excitation characteristics – wavelength, intensity, pulsewidth – will be explained and illustrated by selected experimental results. The final part points out the important role played by thermal effects in the nonlinear optical response

Boron-subphthalocyanines (SubPcs)—cone-shaped 14-π electron aromatic macrocycles—are lower phthalocyanine analogues which consist of three isoindole units N-fused around a central boron atom which fourth valency is occupied by an axial ligand. SubPcs have been shown to possess very interesting features for NLO. Although they present a permanent dipole moment along the boron-axial substituent axis, their optical response is essentially associated to charge transfer inside the macrocycle π-surface. Moreover, due to the C_3v symmetry of the SubPc core, its NLO behavior is mostly octupolar. It will be shown that the application to SubPcs of the design criteria that have been successful in phthalocyanines and porphyrins led to high-performance second-harmonic generators

The NLO properties of iron, ruthenium, osmium, nickel, and gold alkynyl complexes and some related compounds prepared in the authors’ laboratories are reviewed. Structure-property relationships for both quadratic and cubic NLO merit for these complexes have been developed from hyper-Rayleigh scattering studies at 1.064μm and Z-scan studies at 0.800μ m, respectively

This work provides a relatively comprehensive review of studies involving ruthenium coordination and organometallic complexes as nonlinear optical (NLO) compounds/materials, including both quadratic (second-order) and cubic (third-order) effects, as well as dipolar and octupolar chromophores. Such complexes can display very large molecular NLO responses, as characterised by hyperpolarizabilities, and bulk effects such as second harmonic generation have also been observed in some instances. The great diversity of ruthenium chemistry provides an unparalleled variety of chromophoric structures, and facile Ru^II → Ru^III redox processes can allow reversible and very effective switching of both quadratic and cubic NLO effects

Linear and nonlinear optical properties of catenanes and rotaxanes in thin films and in solution are reviewed and discussed. The compounds represent a new class of molecules, with mobile subparts. It offers a new kind of applications, particularly for optical switching. The rotational mobility of the subparts of these molecules was studied by the electro-optic Kerr effect. Both catenanes and rotaxanes can be processed into partly ordered thin films by vacuum sublimation. The degree of order may be controlled by an adequate chemical modification of the molecules, as it was observed in a series of substituted rotaxanes. Methods for controlling the motion of the components using light and electric fields are presented. The linear optical properties were studied by UV-Vis spectrometry and m-lines technique. The nonlinear optical properties were studied in solution and/or in thin films by the optical second and third harmonic generation techniques and by the quadratic electro-optic Kerr effect. The knowledge on the rotaxanes and the catenanes linear and nonlinear optical properties obtained by theses studies is important for the future construction of synthetic molecular machines and optical switching elements

A general review of the second harmonic (SH) light scattered from aqueous suspensions of small gold and silver metallic particles is presented. The first part is devoted to the general theory of the SH generation from particles in order to discuss the incidence of the shape of the particles and the retardation effects of the electromagnetic fields on the total SH scattered field. The next part focuses on the problem of the polarization fields, a problem rather specific to metallic particles. Because of their strong polarizability and the possibility of resonance enhancements through surface plasmon (SP) excitations, the exciting field cannot be taken as the incident field only but rather as the superposition of the incident and the polarization fields. An illustration of this problem is presented with the determination of the exact origin of the SH response from metallic particles. This experimental section presents two different sets of data: the size dependence of the SH intensity and the polarization patterns recorded in the geometrical configuration of Hyper Rayleigh Scattering. SP resonance enhancements of the absolute values of the hyperpolarizabilities are then discussed before a presentation of the SH response of aggregating suspensions of particles and their possible applications is given